{
  "id": "2010.03363",
  "version": "v1",
  "published": "2020-10-07T12:26:58.000Z",
  "updated": "2020-10-07T12:26:58.000Z",
  "title": "Symmetric polynomials associated with numerical semigroups",
  "authors": [
    "Leonid G. Fel"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study a new kind of symmetric polynomials P_n(x_1,...,x_m) of degree n in m real variables, which have arisen in the theory of numerical semigroups. We establish their basic properties and find their representation through the power sums E_k=\\sum_{j=1}^m x_j^k. We observe a visual similarity between normalized polynomials P_n(x_1,...,x_m)/\\chi_m, where \\chi_m=\\prod_{j=1}^m x_j, and a polynomial part of a partition function W(s,{d_1,...,d_m}), which gives a number of partitions of s\\ge 0 into m positive integers d_j, and put forward a conjecture about their relationship.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-07T12:26:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M14",
      "11P81"
    ],
    "keywords": [
      "symmetric polynomials",
      "numerical semigroups",
      "basic properties",
      "power sums",
      "visual similarity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}